In such a machine, with which it is possible to perform embossing functions requiring particularly high quality, during the embossing phase, the embossing foil web must be stopped in an accurately determined position on the embossing table and subsequently, during the non-embossing phase, fed rapidly into the next foil web embossing position. The sensitive embossing foil web must be carefully handled and conveyed. This is difficult to achieve because, as a result of this embossing cycle, there is a very non-uniform feed at the embossing location, while the sluggish unwinding rolls are driven in a substantially uniform manner. The resulting length changes have hitherto been compensated for by floating or dancing rollers. This was possible up to average embossing speeds. However, the foil web speeds, the number of simultaneously processable foil webs and, in particular, the machine speed were limited. Nevertheless, flat-flat embossing geometry permits the highest embossing qualities, particularly for relief printing and for large image formats. An improvement in partial areas could be achieved, e.g., with a register control according to EP-A-708 046 or with an automatic print control according to EP-A-749 001. However, the fundamental limitations still remain.